Minimal genus for 4-manifolds with b+ = 1

Bo Dai; Chung I. Ho; Tian Jun Li

doi:10.1112/jtopol/jtv032

Minimal genus for 4-manifolds with b⁺ = 1

Bo Dai, Chung I. Ho, Tian Jun Li

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We derive an adjunction inequality for any smooth, closed, connected, oriented 4-manifold X with b⁺ = 1. This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case of b₁ = 0. We demonstrate that the inequality is especially powerful when 2^~_χ + 3_σ ≥ 0, where ~χ is the modified Euler number taking account of the cup product on H¹(X;).

Original language	English (US)
Article number	jtv032
Pages (from-to)	5-26
Number of pages	22
Journal	Journal of Topology
Volume	9
Issue number	1
DOIs	https://doi.org/10.1112/jtopol/jtv032
State	Published - Jul 29 2015

Bibliographical note

Publisher Copyright:
© 2015 London Mathematical Society.

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10.1112/jtopol/jtv032

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abstract = "We derive an adjunction inequality for any smooth, closed, connected, oriented 4-manifold X with b+ = 1. This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case of b1 = 0. We demonstrate that the inequality is especially powerful when 2~χ + 3σ ≥ 0, where ~χ is the modified Euler number taking account of the cup product on H1(X;).",

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